Warm Up 11.14.11Week 5

Can the theorems be used to prove triangle congruency?

1) ASA 2) SAS 3) SSA

CA

B

FD

E

Geometry

4.5 Day 1

I will use congruent triangles to plan and write proofs.

Rule 1 Place congruency marks as you prove.

∠A ≅ D ∠

≅

Given:

Given:

Ex 1

F

E

G

H

C

A

B

D

CPCSC Corresponding Parts of Congruent Shapes are Congruent

Ex 2

∠A ≅ E ∠

CPCSC

Statement

Reason

ABCD ≅ EFGH

Given:

∠ABD ≅ CDB ∠

∠ADB ≅ CBD ∠

B

D

C

A

∥Given:

∥Given:

∆ABD ≅ ∆CDBProve:

≅

∆ABD ≅ ∆CDB

Alternate Interior Angles Theorem

Alternate Interior Angles Theorem

Reflexive Property of Congruence

ASA

Ex 3

Statement Reason

   

   

   

   

   

   

Ex 4

Given

Definition of midpoint

Vertical Angles Theorem (2.6)∠MAS ≅ TAR ∠

CPCSC

∆MAS ≅ ∆TAR

Alternate Interior Angles Converse ( T3.8 )

M

S

R

A

T

Given: A is midpoint of

Given: A is midpoint of

Prove: ∥

A is midpoint of and

≅ ≅,

SAS ( P19 )

∠SMA ≅ RTA ∠

∥

Do: 1

Assignment:

Textbook Page 232, 4 - 10 all and 14.

N

M

L

P

Q

≅ Prove: